## normal distribution

pdwary
Posts: 3
Joined: Sun Aug 19, 2012 4:12 pm

### normal distribution

Assume that a random variable follows a normal distribution with a mean of 50 and a standard deviation
of 10. What percentage of this distribution is between 55 and 65?
A. 4.56%
B. 8.96%
C. 18.15%
D. 24.17%

As there is no mention of significance or confidence level ?

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praghavan039
Posts: 4
Joined: Tue Aug 14, 2012 3:59 pm

### Re: normal distribution

I think its 24.17.

Empirical rule: 68-95-99.7
Rule: Normal distribution accounts for 3 standard deviations.
SD 1 - 68% (34 + 34)
SD 2 - 95%
SD 3 - 99.7%

In the problem, Mean - 50, SD - 10. So, drawing normal dist. curve, we take 50 as 0 in mean and 60 as +1 and 40 as -1. So, 55 will be in 0.5 and 65 will be in 1.5

We have to find the z value of 0.5 and 1.5 from Z tables. I think we can find it even with financial calculator.

Z value of 1.5 = 0.9332
Z value of 0.5 = 0.6915
0.9332 - 0.6915 = 0.2417 = 24.17%

Finance Junkie
Posts: 99
Joined: Sat Apr 07, 2012 10:24 am

### Re: normal distribution

In these type of qns, just find out teh Z score.

Z = (X-mean)/sigma

Z1 = (55-50)/10 = 0.5
Z2 = (65-50)/10 = 1.5

So the ans is area lying between 0.5 and 1.5 that is around 24%.

Shortcut: As you know that area under 1 SD (plus, minus 1) is 68%. Here you want area for 1 SD in positive side so half of 88% is just 24% that is the ans. (no need to refer z table)

hope it helps!!